Clearly if a trip is genuinely essential and it needs to be done in a car, then objectively it makes no difference if the car used is a Morgan or anything else.
But this is about perception in the eyes of others. Regardless of the facts of the particular situation, driving a Morgan in times like this carries the risk of being interpreted as 'some rich bloke ignoring the rules out for a jolly' by some people - especially when they see reports of people being stopped for doing a 250-mile trip ostensibly to get some bread.
Personally, I wouldn't want to be responsible for such, so the Morgan stays at home. It's only once a week to the nearest shop for essential supplies, so it's a very short trip anyway so it's not like I'm missing much.
